How should I approach the game "Achtung, Die Kurve" ("Curve Fever") using AI?
Start slowly.
Don't jump straight into Deep Learning, arguably the most complex class in Reinforcement Learning techniques. First work with simpler algorithms, like the original Q-Learning. Define what are good inputs and outputs for your game, and start tuning some hyper-parameters (like future rewards discount factor).
From there, go for Deep Learning. Check other implementations (like DQN, Atari n-step Q-Learning and A3C), and adapt their code to yours, rather than starting from scratch.